Chapter 4: Time Value of Money - The Multiperiod Model 1

arbitrage

the pursuit of riskless profits by identifying deviations from the law of one price and then simultaneously trading to profit from the mispricing

arbitrageur

an individual or firm that tries to create an informational advantage by spotting mispricing across markets, then trading simultaneously in those markets to capture a riskless profit

• trading activity of arbitrageur eliminates the pricing anomaly and enforces the law of one price

binomial tree

a model where the state-contingent outcome at the end of the one period’s model begins the next binomial model, creating a set of paths from the starting point to a range of possible endpoints

• by adding steps, the set of possible paths from the present to the future value increasingly looks like a tree

compound annual growth rate (CAGR)

the annual rate of return that generates an ending balance from a beginning balance if one reinvests the profits at the end of the year

compound interest

interest earned on both the initial principal and the reinvested interest earned in prior periods

compounding

the process of reinvesting earnings to generate interest-on-interest on an investment or debt

consistent

in TVM calculations involving the fundamental equation of finance, you must define both the periodic rate and the number of periods over the same unit of time

• start with the rate and then determine the number of periods between the lump sums

  • if rate is 1% per month, then you must measure the time between the lump sums in months

coupons 

the regular interest-only payments bond issuers make to bondholders

credit/defualt risk

the chance that a borrower will not fulfill their contractural obligations to a lender

discount rate

the interest rate used to calculate the equivalent present value of a future value

discounted cash flow (DCF)

a valuation method that gets the value of an investment’s expected cash flows at a single point of time earlier on a timeline and adds them up

discounting

determining the present value of an expected future cash flow using the discount rate

diversification

the process of reducing risk by spreading investments among a variety of securities that don’t move alike

face value

the known future value a financial security pays out on the maturity date

fixed-rate-loan

a loan where the contract applies the same periodic rate for every period until the borrower pays off the debt at maturuity

fundamental equation of finance (FEF)

the quantitative relationship between the present and future values; the compound periodic rate and number of periods separating the 2 lump sums relate them

• the mathematical relationship between 2 lump sums, which critically depends on the investor’s risk-adjusted opportunity cost and how long they must wait between the contracts outflow and inflow; assumes it is a compound interest contract

future value interest factor

assuming strictly positive interest rates, a number greater than one that transforms a smaller present value into a equivalent larger future value

interest-on-interest

the interest earned on earlier interest payments that became part of the principal balance

law of one price

the Rule that similar assets should have similar prices

• violations of the law of one price create profitable opportunities for investors who spot the resulting misprcing

  • in equilibrium, the resulting profit-seeking trading activity restores the law of one price

maturity date

the date in a debt contract when the borrower fulfills the repayment of the loan’s principal to the lender; if the borrower satisfies the debt contract’s term, the maturity date ends the relationship between the lender and borrower

monte carlo simulation

a class of computational tecnhiques that rely on repeated random sampling to estimate the outcomes of uncertain processes, such as the cash flows that financial securities and projects generate through time

mortgage

a debt instrument where the lender holds the title for the property until the borrower pays off the loan; in this arrangement, the property is the loan’s collateral

• norm in loans involving real assets such as residential homes, land, and commercial properties

net present value (NPV)

the present value of cash inflows minus the present value of cash outflows

net present value rule

accept all positive NPV investments because they cost you less than they are worth, thus creating shareholder wealth

• reject all value-destroying negative NPV investments; and indifferent to 0 NPV because they don’t create or destroy value

node

a point in a binomial tree where a realized outcome is the beginning of the next one-period binomial step

number of periods (t)

the number of periods between the two lump sums and is consistent with the periodic rate

• ex: if a contract calculates interest on a quarterly basis, the time that separates the cash flows must be measured in quarters

periodic interest rate/periodic rate (r)

the nominal interest rate defined in a contract that specifically states how much interest is earned or paid over an interval of time, be it a simple or compound interest contract

portfolio

a collection of assets held by an individual or organization that seeks risk reduction by holding assets whose comovements are not perfectly correlated

present value interest factor

assuming strictly positive interest rates, a number less than one that transforms a larger future value into an equivalent smaller present value

pure discount loan/bond/zero-coupon bond

the simplest possible loan that involves 2 cash flows; initially the principal changes hands, and then the borrower pays back the principal and interest with a single payment at a later date

• t-bills, commerical paper, and savings bonds

random walk

a process that describes a path of successive random steps over time

• has no memory in the sense that the path that leads to a particular node in the binomial tree has no predictive power as to where the next step will land (independent trail)

rule of 72

divide 72 by an interest rate in its percentage form to approximate the time to double one’s money

simple interest

the interest an investment earns or loan pays on the original principal only

stochastic process

a sequence of random variables revealed over time; produces outcomes that jump around, making a discontinuous function

zero-coupon bond

a pure discount bond

• t-bills